Direct Measurements of Binary Gas Phase Diffusion ...€¦ · High flow rates, reasonable sampling times. Katsanos and Karaiskakis (1982). J. of Chromatography . 237 (1): 1-14. where,

1

Direct Measurements of Binary Gas Phase Diffusion

Coefficients for Combustion Applications

MACCCR Fuels Research ReviewArgonne National Laboratory

Darien, IL September 21, 2011

Jeffrey A. Manion (NIST)W. Sean McGivern (NIST)

Support:AFOSR

2

Motivation and Background

Simulations require diffusivities in a variety of situations:

Laminar diffusion flames: - preferential species diffusion affects flame structure & attributes

Laminar premixed H2-air flames: computed flame speed as sensitive to diffusion as kinetics of the primary chain branching reaction

Turbulent flames: small scale structures are affected by diffusion.

Premixed alcohol, n-heptane, and iso-octane/air flames: sensitivity of flame speeds and extinction strain rates to diffusion can be of the same order as to the kinetics.

Takagi; Xu; Komiyama, Comb. & Flame, 1996, 106, 252.Takagi; Xu, Comb. & Flame, 1994. 96, 50.

Harstad, Bellan, Ind. & Eng. Chem.Res., 2004. 43, 645.Okong'o, Harstad, Bellan, AIAA Journal, 2002. 40, 914.Okong'o; Bellan, J. Fluid Mech., 2002. 464, 1.

Holley, Dong; Andac; Egolfopoulos, Comb. & Flame, 2006. 144, 448.

Wang, Chem. Phys. Let., 2000. 325, 661.

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Topics

Measurement Methods & Apparatus

System Characterization

n‐alkanes

Cyclic & Branched Alkanes

Summary

4

Diffusion Measurement Methods ‐ Historical

Watch concentration change as f(time)

Watch width increase as slowly flows through (very) long tube

InjectionFlow

1. Closed tube

3. Gas Chromatography‐ Peak Broadening

2. Two‐bulb

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Gas Chromatographic Method II

1) Take a gas‐filled tube of known length in which no flow occurs and which is open at one end

Basic Idea:

SubstrateInjection

Static Diffusion ColumnEntraining gas flow to GC detector

Re(max) = 12

2) Inject substrate at closed end and let it diffuse

3) Monitor time‐dependent concentration exiting open end

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Diffusion Measurement ‐ GC Method II

Monitor concentration – time profile at exit of static diffusion column

Katsanos and Karaiskakis (1982). J. of Chromatography 237(1): 1‐14.

Static

Flow

Inject(t0)

Detector Signal

Time

Baseline drift causes systematic errors Flow Reversal Methods

Separates diffusive and analytical fluxes; no valves at high T

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Baseline Correction with Flow Reversal

Timescales of hours

Reversals done every few minutesConstant drift correction

Typical FIDs and TCDs show a small drift over the several hours required for many analyses

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ApparatusSome Details:1. Valve operation, oven T controlled by GC and automated2. Diffusion columns 61 cm or 23 cm 4.6 mm I.D. electropolished 316 SS3. Starting hydrocarbon concentrations (2 to 4)%4. Experimental pressures ca. 2 - 4 bar5. ca. 0.2 ml injection volumes

FIDorTCD

Oven GCAnalytical GC

Diffusion Column

InjectionValve

FlowReversalValve

VacuumSample Loop

Aux Gas (sample injection)

Carrier Gas

Restrictor Valve

Sampling Column

Sample

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Mathematical Analysis ‐ I

1. Relate concentration-time profile of substrate along diffusion tube to diffusion coefficient (Fick’s second law)

2. Relate detector signal to concentration-time profile of substrate at exit of diffusion tube

3. Describe effects of flow reversals

FID

Flow

Sta

tic

FID

Flow

Sta

tic

FID

Flow

Sta

tic

SubstrateInjection

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Mathematical Analysis ‐ II

2

2

zcD

tc z

ABz

∂∂

=∂∂

t = time measured from injection of the substrate z = distance coordinate along diffusion tubec = concentration of the substrate ADAB = binary diffusion coefficient

Fick’s Second Law

h = peak height N = constantL = length of diffusion tubeτ = relates peak elution time to the time the

substrate exits diffusion tube

t0 = peak elution time measured from injection of substrate

tM = gas hold-up timetFR = duration of flow reversal

Assumptions:1. Only gas phase diffusive flow (no convection, thermal gradients, wall interactions)2. Initial mass distribution of substrate is a delta function3. No diffusion in sampling column4. High flow rates, reasonable sampling times

Katsanos and Karaiskakis (1982). J. of Chromatography 237(1): 1-14.

where,

( )[ ]( ) 23

2 4expτ

τABDLNh −=

FRM ttt 210 −−=τ

Result:

FID

Sta

ticZ = 0

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Example Data Plot

Figure 2. Plot of equation for an experiment with C2H6 – N2 at 350 K.

( )τ

τ 14

lnln2

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ABDLNh −=Laplace Transform Result:

Katsanos and Karaiskakis (1982). J. of Chromatography 237(1): 1‐14.

12

Laplace Transform Analysis Not Valid at Long Times

Dilute CH4 in He at 599.9 KD (1.013 bar) = (2.146 ± 0.011) cm2 s–1

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tnttzizz

n

i

Δ+=Δ+=

0

0

2

2

zcD

tc

∂∂

=∂∂

( ) ⎥⎦⎤

⎢⎣

⎡

Δ+−++−

=Δ− +−+++−++

211111111 ),(),(2),(),(),(2),(

2),(),(

ztzctzctzctzctzctzcD

ttzctzc nininininininini

Crank‐Nicholson solution for c(z,t)

Crank‐Nicholson Numerical Simulation

0

0

==

==

=⎟⎠⎞

⎜⎝⎛∂∂

−

=

xxLz

z

xxLxz

vctcD

cc0=z

Lz =

0=xlx =

Except for reversals (not considered here),There is no sample transfer from x

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Diffusion Coefficient Determination

Dilute CH4 in He at 599.9 KD (1.013 bar) = (2.146 ± 0.011) cm2 s–1

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TopicsMeasurement Methods & Apparatus


n‐alkanes


Summary

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Effect of Distribution of Injected Sample

Numerical simulations

Examined for Range of Typical D values

Sample DistributionsSquare wave

0.25 ml ‐ Simulated D within 0.05% of input value

1.0 ml – Simulated D within 1.5 % of input value

½ Gaussian wave



Results suggest minimal errors for low injection volumes Injection volume set at 0.2 ml

Injection pressure differential kept low (6 sec injection time)

Custom fitting to deliver sample precisely at end wall

Square wave

½ Gaussian

SubstrateInjection

Static Diffusion Column

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Uncertainties and Effective Tube Length: Calibration with Noble Gas (He/Ar) Reference

(60.79 ± 0.01) cm

61.5 cm at calculated midpoint (assuming …) Up to 0.23 cm

DHe‐Ar = (0.7344 ± 0.0042) cm2 s–1 at 1.013 bar and 300 K (2σ uncertainty)[17] W.A. Wakeham, A. Nagashima, J.V. Sengers, Experimental Thermodynamics, Vol. III: Measurement of the Transport Properties of Fluids. Blackwell Scientific: Oxford, 1991; p 459.

Effective L=(61.28±0.01) cm

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Dilute Argon in Helium

2σ uncertaintiesour points are avg. of 5‐10 runsall D scaled linearly to 1 atm

]s[cm )K 1/(10)24.034.5()( 12007.0674.1512−±−×±= TTD

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Dilute He‐Ar vs Dilute Ar‐He

Demonstrates ability to measure small differences in D values. Suggests accuracy to within 1.5%

W. A. Wakeham; A. Nagashima, J.V. Sengers, Experimental Thermodynamics, Vol. III: Measurements of the Transport Properties of Fluids, Blackwell Scientific, Oxford, 1991.

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n‐Alkanes


Summary

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Methane in Helium

leftright

P. J. Dunlop; C. M. Bignell, J. Chem. Phys. 1990, 93, (4), 2701‐2703. ‐ Two bulb method (“gold standard”)

A. C. Frost. A Method for the Measurement of Binary Gas Diffusivities. Columbia University, 1967. – Modified Stefan cell.Marrero, E. R.; Mason, E. A. Journal Of Physical And Chemical Reference Data 1972, 1, 3.. – Review.

Frost diffusion cell

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Normal Butane in HeliumP. J. Dunlop; C. M. Bignell, J. Chem. Phys. 1990, 93, (4), 2701‐2703 ‐ Two bulb method (“gold standard”)

A. C. Frost. A Method for the Measurement of Binary Gas Diffusivities. Columbia University, 1967. – Modified Stefan cell

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Butane in NitrogenW. A. Wakeham; D. H. Slater, J. Phys. B: At. Mol. Opt. Phys. 1973, 6, (5), 886‐896. – GC peak broadening method.

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n‐Pentane in Helium

This work: Dn-Pentane-He(300-600 K) = 2.62x10-5 T1.637

At 1000 K, our D is about 50% smaller than the Hargrove/Sawyer value

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n‐Hexane in Helium

At 1000 K, our D is about 40% smaller than the Hargrove/Sawyer value

Substrate “sticks” at low T

Δt

Changes in chromatogram at 300 K indicate sticking to walls:1. Δt changes (should be constant)2. Peak shape becomes poor

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Diffusion Coefficients of Hydrocarbons in He and N2

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Temperature Dependence of DnaTTD =)( (T in K)

n(N2) > n(He)

Little variation in n for C2 to C5 between 300 K and 723 K

Does extrapolation hold to higher T, e.g. 2000 K?

Raymond D. Mountain, Molecular Dynamics Determination of Mutual Diffusion Coefficients of Gases: Ethane in Nitrogen., (manuscript under preparation)

MD simulations suggest yes

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Alkane Diffusion in He vs. N2

Variation in D(He)/D(N2) at 300 K

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n‐alkanes


Summary

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Diffusion of C5 Isomers

Little variation with branching for C5

Increase in D for cyclopentane probably mostly a mass effect

% Difference in D relative to NeopentaneD Values at 350.15 K

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Diffusion of C8 Isomers

Grushka & Maynard find 9 % variation in D for C8 series at 373 K

We find D(hexamethylethane) ≈ 1.15D(n‐octane)

(most spherical vs. most linear)

Our absolute D for n‐octane is 10% smaller than Grushka/Maynard

% Difference in D relative to n-octaneLit. D Values at 373 K

Grushka & Maynard, J. Phys. Chem. 1973, 77, (11), 1437‐1432. – Peak Broadening

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Isomer effect not fully resolvedGrushka & Maynard:

9 % variation in D for C8 series at 373 K

Single methyl branch has large effect

Chae & Violi (MD simulations)6% variation for C7 Series

Single methyl branch has little effect; some variation with T

Present workLittle variation for C5H12 series (2% difference)

(12 to 15)% increase in D for:

hexamethylethane vs. n‐octane

Need to examine other C8’s and C7 series

Grushka & Maynard, J. Phys. Chem. 1973, 77, (11), 1437‐1432. – Peak Broadening

Chae & Violi, J. Chem. Phys. 2011, 134, 044537.

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Summary & Future DirectionsCurrent Status

D within 2% accuracy for well‐behaved substrates, 300 – 725 K.

Data show consistent n values for He and N2 when using D = aTn form.

Branching appears to increase D somewhat; magnitude of effect not fully

resolved but may increase with molecular size.

Sticking (low T) & decomposition (high T) are experimental issues for larger

compounds; Compounds > C8 remain a challenge.

Automation of data collection is (finally) robust.

Future Directions:

Complete C1 – C8 hydrocarbon matrix

Further examine geometrical effects for selected Cn

Examine other substituent classes

Resolve issues with larger species measurements

Direct Measurements of Binary Gas Phase Diffusion Coefficients for Combustion Applications Motivation and Background TopicsDiffusion Measurement Methods - HistoricalGas Chromatographic Method IIDiffusion Measurement - GC Method IIBaseline Correction with Flow ReversalApparatusMathematical Analysis - IMathematical Analysis - IIExample Data PlotLaplace Transform Analysis Not Valid at Long TimesCrank-Nicholson Numerical SimulationDiffusion Coefficient DeterminationTopicsEffect of Distribution of Injected SampleUncertainties and Effective Tube Length: �Calibration with Noble Gas (He/Ar) ReferenceDilute Argon in HeliumDilute He-Ar vs Dilute Ar-HeTopicsMethane in HeliumNormal Butane in HeliumButane in Nitrogenn-Pentane in Helium n-Hexane in Helium Diffusion Coefficients of Hydrocarbons in He and N2Temperature Dependence of DAlkane Diffusion in He vs. N2TopicsDiffusion of C5 IsomersDiffusion of C8 IsomersIsomer effect not fully resolvedSummary & Future Directions

Documents

Direct Measurements of Binary Gas Phase Diffusion ...€¦ · High flow rates, reasonable sampling times. Katsanos and Karaiskakis (1982). J. of Chromatography . 237 (1): 1-14. where,